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Joint Optic Disc and Cup Segmentation Based on Multi-label Deep Network and Polar Transformation

Huazhu Fu, Jun Cheng, Yanwu Xu, Damon Wing Kee Wong, Jiang Liu, Xiaochun Cao

arXiv:1801.00926v3cs.CV

TL;DR

Accurate automatic optic disc and cup segmentation is needed for glaucoma screening, but existing approaches often segment them separately and rely on hand-crafted features. The paper proposes M-Net, a one-stage multi-label deep network enhanced with polar transformation. M-Net achieves state-of-the-art optic disc and cup segmentation on ORIGA and satisfactory CDR-based screening on ORIGA and SCES.

  • Problem

    Automatic optic disc and cup segmentation is needed for glaucoma screening because CDR is important, while many existing methods segment the regions separately and rely on hand-crafted features.

  • Method

    M-Net jointly segments optic disc and cup regions using multi-scale inputs, a U-shape network, side-output supervision, and a Dice-based multi-label loss, with polar transformation as an additional representation.

  • Results

    M-Net with polar transformation achieves the best reported glaucoma-screening AUCs on ORIGA (0.8508) and SCES (0.8997), with more than 5% improvement over M-Net without polar transformation.

  • Takeaways & Limitations

    The system supports joint OD/OC segmentation and CDR-based glaucoma screening across the ORIGA and SCES datasets.

Abstract

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Glaucoma is a chronic eye disease that leads to irreversible vision loss. The cup to disc ratio (CDR) plays an important role in the screening and diagnosis of glaucoma. Thus, the accurate and automatic segmentation of optic disc (OD) and optic cup (OC) from fundus images is a fundamental task. Most existing methods segment them separately, and rely on hand-crafted visual feature from fundus images. In this paper, we propose a deep learning architecture, named M-Net, which solves the OD and OC segmentation jointly in a one-stage multi-label system. The proposed M-Net mainly consists of multi-scale input layer, U-shape convolutional network, side-output layer, and multi-label loss function. The multi-scale input layer constructs an image pyramid to achieve multiple level receptive field sizes. The U-shape convolutional network is employed as the main body network structure to learn the rich hierarchical representation, while the side-output layer acts as an early classifier that produces a companion local prediction map for different scale layers. Finally, a multi-label loss function is proposed to generate the final segmentation map. For improving the segmentation performance further, we also introduce the polar transformation, which provides the representation of the original image in the polar coordinate system. The experiments show that our M-Net system achieves state-of-the-art OD and OC segmentation result on ORIGA dataset. Simultaneously, the proposed method also obtains the satisfactory glaucoma screening performances with calculated CDR value on both ORIGA and SCES datasets.

I. INTRODUCTION

Glaucoma screening requires accurate optic disc and optic cup segmentation because CDR is clinically used, yet manual assessment is costly and existing approaches motivate an automatic multi-label deep network.

  • Glaucoma is a major cause of irreversible blindness, making early screening and detection important for preserving vision and quality of life.
  • Manual optic nerve head assessment is time consuming and costly, limiting its suitability for population screening.
  • CDR, calculated from vertical cup and disc diameters, is a commonly accepted clinical measurement for glaucoma screening.
  • Deep learning successes in fundus-image analysis motivate investigating it for optic disc and cup segmentation.
  • The paper formulates joint optic disc and cup segmentation as a multi-label task solved by an end-to-end deep network.
  • M-Net combines a multi-scale U-shape network, side-output layer, Dice-based multi-label loss, and polar transformation, achieving ORIGA average overlapping errors of 0.07 for OD and 0.23 for OC.

II. RELATED WORKS

Earlier optic disc and cup methods use templates, geometric cues, hand-crafted features, or separate stages, while the paper presents a joint M-Net and polar-transformation framework.

  • Optic Disc Segmentation: Earlier optic disc segmentation methods include template-based, circular-transformation, local-texture, and pixel-classification approaches.
  • Optic Disc Segmentation: Hand-crafted visual features are used by superpixel-based optic disc and cup segmentation methods.
  • Optic Cup Segmentation: Optic cup segmentation is challenging because its boundary has low contrast, and vessel-bend cues can be confounded by natural vessel bending.
  • Joint OD and OC Segmentation: Most existing methods focus on one region or use separate stages, whereas joint segmentation can exploit the mutual relation between optic disc and cup.
  • Proposed Framework: The proposed pipeline localizes the disc center, applies polar transformation, feeds the image to M-Net, and inverse-transforms predictions to Cartesian coordinates.

A. M-Net Architecture

M-Net is an end-to-end multi-label architecture that combines multi-scale inputs, a U-shape convolutional network, side-output supervision, and joint OD/OC classification.

  • M-Net has four main components: a multi-scale layer, U-shape convolutional network, side-output layer, and multi-label loss function.
  • The multi-scale layer constructs an image pyramid and fuses multiple receptive-field levels.
  • The U-shape network serves as the main body for learning hierarchical representations through encoder and decoder paths.
  • A trainable 1 × 1 convolutional classifier with sigmoid activation produces pixel-wise K-channel probability maps, with K = 2 for OD and OC.

2) Multi-scale Input Layer:

M-Net integrates multi-scale inputs into the encoder path and uses side-output supervision to combine predictions across scales while supporting early-layer training.

  • Multi-scale Input Layer: The multi-scale input layer uses average pooling to construct an image pyramid naturally within the encoder path.
  • Multi-scale Input Layer: Integrating multi-scale inputs into decoder layers avoids large parameter growth and increases decoder-path width.
  • Side-output Layer: Side-output layers produce companion local prediction maps for early convolutional layers.
  • Side-output Layer: Each side-output loss is fused with weight αm = 0.25, and an average layer combines side-output maps into the final prediction map.
  • Side-output Layer: Side-output supervision propagates loss to early decoder layers and supports multi-scale prediction fusion.

4) Multi-label Loss Function:

The paper formulates optic disc and optic cup segmentation as a multi-label problem and uses a Dice-based loss to handle overlapping labels and pixel imbalance.

  • Multi-label segmentation assigns independent binary labels, allowing cup pixels to simultaneously carry optic disc and optic cup labels.This represents the overlap between the disc and cup regions directly.
  • The proposed loss is based on the Dice coefficient and is designed for multi-label, pixel-wise segmentation.The Dice coefficient measures overlap between predicted and ground-truth masks.
  • With K = 2, the loss separately models optic disc and optic cup segmentation using class weights that sum to 1.The paper sets both class weights to 0.5 for glaucoma screening.
  • Dice loss addresses foreground–background pixel imbalance by measuring foreground-mask overlap.The formulation uses predicted probabilities and binary ground-truth labels for each class.
  • The loss is integrated into back-propagation through standard stochastic gradient descent.

B. Polar Transformation for Fundus Image

The method transforms fundus images into polar coordinates centered on the optic disc, converting cup–disc geometry into an ordered spatial structure for joint segmentation.

  • Polar transformation maps each Cartesian pixel p(u, v) to a polar point p′(θ, r) centered at the optic disc.Here, r is the radius and θ is the directional angle.
  • In polar coordinates, cup, disc, and background form an ordered layer-like structure that makes their spatial relationship easier to use.The optic cup remains within the optic disc, but this constraint is difficult to implement directly in Cartesian coordinates.
  • The transferred polar image uses transformation radius R as its height and angular discretization 2π as its width.
  • Because the mapping is pixel-wise, augmentation in the original image has an equivalent representation in polar coordinates.For example, moving the expansion center corresponds to drift cropping in polar coordinates.
  • Unlike prior polar use for detecting cup edges from stereo depth, this method uses polar coordinates for spatial constraints and joint OD–OC segmentation.

IV. EXPERIMENTS

Experiments evaluate OD/OC segmentation on ORIGA, compare M-Net with established methods and variants, and assess visual quality and glaucoma screening using CDR. Polar transformation improves segmentation, while blurred low-contrast cases remain challenging.

  • Segmentation Experiments: The ORIGA experiments evaluate OD and OC segmentation using overlapping error and balanced accuracy, alongside CDR-based glaucoma screening.The study uses 325 training and 325 testing images for segmentation, with ROC curves and AUC scores reported for ORIGA and SCES screening.
  • Segmentation Experiments: Joint U-Net outperforms traditional U-Net, while M-Net’s multi-scale input and side-output layers outperform the single-scale network and superpixel method.The reported comparison links these gains to mutual OD/OC information and guidance of early-layer training.
  • Segmentation Experiments: M-Net with polar transformation achieves the best performance among the compared segmentation methods on ORIGA.The comparison includes traditional approaches, U-Net variants, Joint U-Net, and M-Net with and without polar transformation.
  • Segmentation Experiments: 0.03 and 0.02 reductions in Ecup are reported for Joint U-Net and M-Net, respectively, after adding polar transformation.The authors attribute the improvement to a more balanced representation of disc, cup, and background regions.
  • Segmentation Experiments: All methods fail to produce accurate optic-cup segmentation in a blurred, low-contrast example.The visual examples include fundus images, ground truth, Joint U-Net, M-Net, and M-Net with polar transformation; M-Net with PT is described as effective on other cases.

C. Glaucoma Screening

The method is evaluated for glaucoma screening using CDR on ORIGA and SCES, with M-Net plus polar transformation achieving the strongest reported AUCs on both datasets.

  • Superpixel achieves AUC = 0.814 on ORIGA, exceeding M-Net's AUC = 0.8014 on that dataset.
  • M-Net with polar transformation achieves the best screening performance on ORIGA and SCES, with AUCs of 0.8508 and 0.8997, respectively.Polar transformation improves AUC by more than 5% over M-Net without polar transformation.
  • Joint U-Net with polar transformation scores higher than superpixel and U-Net on both ORIGA and SCES datasets.
  • The repeatability experiment uses 1520 corresponding fundus-image pairs from two sets, with one image from each pair selected from the same visit.

1) Running Time:

The method requires about five hours for offline training but generates one fundus-image segmentation map in 0.5 seconds during online testing.

  • 0.5s is required to generate one final segmentation map during online testing.Training takes about 5 hours on a single NVIDIA Titan X GPU for 100 iterations.
  • 0.5s online testing is faster than superpixel at 10s, ASM at 4s, R-Bend at 4s, and sequential original U-Net segmentation at 1s.
  • The training phase can be performed offline.

3) Clinical Measurement:

Because M-Net segments whole optic-disc and optic-cup regions, it supports multiple clinical measurements; its polar-transformed version performs best with RDAR on both datasets, while CDR performs better than RDAR.

  • M-Net with polar transformation obtains the best glaucoma-screening performance based on RDAR on both ORIGA and SCES.The comparison is reported in Table III, which defines RDAR as rim-to-disc area ratio.
  • CDR provides better screening performance than RDAR.
  • Whole OD and OC segmentation can be used to calculate other clinical measurements beyond CDR.
  • The rim error is larger than the cup error for M-Net with polar transformation, with E_rim = 0.233 and E_cup = 0.230.Rim estimation inherits errors from both disc and cup segmentation because the rim is computed by subtracting cup from disc.
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